Talk:Implication

Certainty of outcomes Vs possibility of outcomes?

I'm sill a little new to this whole wiki editing thing so i thought i'd better make it a discussion rather than put my foot in it by changing the page willy-nilly.
Where you've written "if P is false, then P → Q is true." would it not be more accurate to say "if P is false, then P → Q may still be true."? after all, if (P), or (P and Q) are both false as per the last two rows in the table, we don't necessarily know that P → Q is true, just that it might be true and that we have insufficient data to rule it out. --Murphy 20:04, 7 November 2009 (CST)

I think I know where you're going with this...

Material implication explores the possibility of Q and ¬Q in the presence of P and ¬P.

Logical implication explores the causative effect of P and ¬P on Q and ¬Q.

The information and example is attempting to explain both material and logical implication in the context of material implication alone. Thus, the article as a whole could seem to be saying ¬P ⇒ (P ⇒ Q), which is false.

Material Implication

Logical Implication

P → Q

P ⇒ Q

P

Q

Valid

P demands Q

Valid

P causes Q

P

¬Q

Invalid

P prevents ¬Q

Invalid

P cannot cause ¬Q

¬P

Q

Valid

¬P allows Q

Invalid

¬P is not the cause of Q

¬P

¬Q

Valid

¬P allows ¬Q

Invalid

¬P is not the cause of ¬Q

¬P allows either Q or ¬Q, but does not cause either.

You could explain the difference between the two, and perhaps even include the chart/info I just wrote.

Another level of confusion for the already confused creationists :) --Jaban 15:52, 8 November 2009 (CST)